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Zbl 0727.60024
Ruciński, Andrzej; Voigt, Bernd
A local limit theorem for generalized Stirling numbers.
(English)
[J] Rev. Roum. Math. Pures Appl. 35, No.2, 161-172 (1990). ISSN 0035-3965

Authors' summary: We consider triangular arrays $S\sp n\sb k(a)$ of reals defined by the inversion $x\sp n=\sum\sp{n}\sb{k=0}S\sp n\sb k(a)(x-a\sb 0)\cdots (x-a\sb k),$ $n=0,1,\dots$, and establish the local limit theorem in case $a\sb 0,a\sb 1,\dots$ is an arithmetic progression. Additionally, the numbers $\sum\sp{n}\sb{k=0}S\sp n\sb k(a)$ are asymptotically evaluated. For a geometric progression $a\sb 0,a\sb 1,\dots$ not even a central limit theorem does hold.
[Peter Schatte (Freiberg)]
MSC 2000:
*60F05 Weak limit theorems
11B73 Bell and Stirling numbers

Keywords: triangular arrays; local limit theorem; generalized Stirling numbers; arithmetic progression; geometric progression; central limit theorem

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